Fisher information is employed as an information-theoretic metric in the cost. The Fisher Information Matrix (FIM) [1]} is a measure of the amount of information given by an observation \(\tilde{y}\)  about a parameter of interest, \(\theta \) .
Assuming that there is no process noise in the parameter model, i.e., \(\theta _{k+1} = \theta _k\) , and due to the Gaussian nature of the measurement noise and linear measurement model, over time \(t_0..,t_N\) , the FIM is
\(\mathbf {F} = \sum _{k = 0} ^{N}\mathbf {H}(t_k)^T \mathbf {\Sigma }^{-1} \mathbf {H}(t_k)\) 
\( {\begin{array}{c}\mathbf {H}(t_k) = \frac{\partial h(\mathbf {x}(t_k),\mathbf {u}(t_k),\theta ) }{\partial \theta } +\\ \frac{\partial h(\mathbf {x}(t_k),\mathbf {u}(t_k),\theta )}{\partial \mathbf {x}}\cdot \frac{\partial \mathbf {x}(\mathbf {x}(t_k),\mathbf {u}(t_k),\theta ) }{\partial \theta }.\end{array}} \) 
